Lisa is building a garden in her backyard in the shape of a right triangle and wants to put a fence around it to keep her dog out. The longest side of the garden is 20 ft and one of the shorter sides is 9 ft. How long does the 3rd piece of the fence have to be?

Round this value however you need to. The exact length is sqrt(319)

In other words, sqrt(319) = 17.8606

Work Shown:

Apply the pythagorean theorem to solve for b.

a^2+b^2 = c^2

9^2 + b^2 = 20^2

81 + b^2 = 400

b^2 = 400-81

b^2 = 319

b = sqrt(319)

b = 17.8606 which is approximate

I'm going with the approximate value it makes more sense to do so in this case. Saying "the length is sqrt(319)" to someone not familiar with math, would probably not convey just how long the third side must be. Round the value in bold however you need to.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

that is the sum

step-by-step explanation:

there are no other answers without knowing the variables values